2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
5 * Use of this software is governed by the GNU LGPLv2.1 license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
10 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 #include <isl_constraint.h>
14 #include <isl_dim_private.h>
16 #include "isl_map_private.h"
18 static unsigned n(struct isl_constraint *c, enum isl_dim_type type)
20 return isl_basic_map_dim(c->bmap, type);
23 static unsigned offset(struct isl_constraint *c, enum isl_dim_type type)
25 struct isl_dim *dim = c->bmap->dim;
27 case isl_dim_param: return 1;
28 case isl_dim_in: return 1 + dim->nparam;
29 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
30 case isl_dim_div: return 1 + dim->nparam + dim->n_in + dim->n_out;
35 static unsigned basic_set_offset(struct isl_basic_set *bset,
36 enum isl_dim_type type)
38 struct isl_dim *dim = bset->dim;
40 case isl_dim_param: return 1;
41 case isl_dim_in: return 1 + dim->nparam;
42 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
43 case isl_dim_div: return 1 + dim->nparam + dim->n_in + dim->n_out;
48 struct isl_constraint *isl_basic_map_constraint(struct isl_basic_map *bmap,
51 struct isl_constraint *constraint;
56 constraint = isl_alloc_type(bmap->ctx, struct isl_constraint);
60 constraint->ctx = bmap->ctx;
61 isl_ctx_ref(constraint->ctx);
63 constraint->bmap = bmap;
64 constraint->line = line;
68 isl_basic_map_free(bmap);
72 struct isl_constraint *isl_basic_set_constraint(struct isl_basic_set *bset,
75 return isl_basic_map_constraint((struct isl_basic_map *)bset, line);
78 struct isl_constraint *isl_equality_alloc(struct isl_dim *dim)
80 struct isl_basic_map *bmap;
85 bmap = isl_basic_map_alloc_dim(dim, 0, 1, 0);
89 isl_basic_map_alloc_equality(bmap);
90 isl_seq_clr(bmap->eq[0], 1 + isl_basic_map_total_dim(bmap));
91 return isl_basic_map_constraint(bmap, &bmap->eq[0]);
94 struct isl_constraint *isl_inequality_alloc(struct isl_dim *dim)
96 struct isl_basic_map *bmap;
101 bmap = isl_basic_map_alloc_dim(dim, 0, 0, 1);
105 isl_basic_map_alloc_inequality(bmap);
106 isl_seq_clr(bmap->ineq[0], 1 + isl_basic_map_total_dim(bmap));
107 return isl_basic_map_constraint(bmap, &bmap->ineq[0]);
110 struct isl_constraint *isl_constraint_dup(struct isl_constraint *c)
112 struct isl_basic_map *bmap;
119 eq = c->line < c->bmap->eq + c->bmap->n_eq;
120 i = eq ? c->line - c->bmap->eq : c->line - c->bmap->ineq;
121 bmap = isl_basic_map_copy(c->bmap);
124 return isl_basic_map_constraint(bmap, eq ? bmap->eq + i : bmap->ineq + i);
127 struct isl_constraint *isl_constraint_cow(struct isl_constraint *c)
135 return isl_constraint_dup(c);
138 struct isl_constraint *isl_constraint_copy(struct isl_constraint *constraint)
147 void isl_constraint_free(struct isl_constraint *c)
155 isl_basic_map_free(c->bmap);
156 isl_ctx_deref(c->ctx);
160 __isl_give isl_constraint *isl_basic_map_first_constraint(
161 __isl_take isl_basic_map *bmap)
167 return isl_basic_map_constraint(bmap, &bmap->eq[0]);
169 if (bmap->n_ineq > 0)
170 return isl_basic_map_constraint(bmap, &bmap->ineq[0]);
172 isl_basic_map_free(bmap);
176 __isl_give isl_constraint *isl_basic_set_first_constraint(
177 __isl_take isl_basic_set *bset)
179 return isl_basic_map_first_constraint((struct isl_basic_map *)bset);
182 struct isl_constraint *isl_constraint_next(struct isl_constraint *c)
184 c = isl_constraint_cow(c);
185 if (c->line >= c->bmap->eq) {
187 if (c->line < c->bmap->eq + c->bmap->n_eq)
189 c->line = c->bmap->ineq;
192 if (c->line < c->bmap->ineq + c->bmap->n_ineq)
194 isl_constraint_free(c);
198 int isl_basic_map_foreach_constraint(__isl_keep isl_basic_map *bmap,
199 int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
202 struct isl_constraint *c;
207 isl_assert(bmap->ctx, ISL_F_ISSET(bmap, ISL_BASIC_MAP_FINAL),
210 for (i = 0; i < bmap->n_eq; ++i) {
211 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
219 for (i = 0; i < bmap->n_ineq; ++i) {
220 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
231 int isl_basic_set_foreach_constraint(__isl_keep isl_basic_set *bset,
232 int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
234 return isl_basic_map_foreach_constraint((isl_basic_map *)bset, fn, user);
237 int isl_constraint_is_equal(struct isl_constraint *constraint1,
238 struct isl_constraint *constraint2)
240 if (!constraint1 || !constraint2)
242 return constraint1->bmap == constraint2->bmap &&
243 constraint1->line == constraint2->line;
246 struct isl_basic_map *isl_basic_map_add_constraint(
247 struct isl_basic_map *bmap, struct isl_constraint *constraint)
249 if (!bmap || !constraint)
252 isl_assert(constraint->ctx,
253 isl_dim_equal(bmap->dim, constraint->bmap->dim), goto error);
255 bmap = isl_basic_map_intersect(bmap,
256 isl_basic_map_from_constraint(constraint));
259 isl_basic_map_free(bmap);
260 isl_constraint_free(constraint);
264 struct isl_basic_set *isl_basic_set_add_constraint(
265 struct isl_basic_set *bset, struct isl_constraint *constraint)
267 return (struct isl_basic_set *)
268 isl_basic_map_add_constraint((struct isl_basic_map *)bset,
272 struct isl_constraint *isl_constraint_add_div(struct isl_constraint *constraint,
273 struct isl_div *div, int *pos)
275 if (!constraint || !div)
278 isl_assert(constraint->ctx,
279 isl_dim_equal(div->bmap->dim, constraint->bmap->dim), goto error);
280 isl_assert(constraint->ctx,
281 constraint->bmap->n_eq + constraint->bmap->n_ineq == 1, goto error);
283 constraint->bmap = isl_basic_map_cow(constraint->bmap);
284 constraint->bmap = isl_basic_map_extend_dim(constraint->bmap,
285 isl_dim_copy(constraint->bmap->dim), 1, 0, 0);
286 if (!constraint->bmap)
288 constraint->line = &constraint->bmap->ineq[0];
289 *pos = isl_basic_map_alloc_div(constraint->bmap);
292 isl_seq_cpy(constraint->bmap->div[*pos], div->line[0],
293 1 + 1 + isl_basic_map_total_dim(constraint->bmap));
297 isl_constraint_free(constraint);
302 int isl_constraint_dim(struct isl_constraint *constraint,
303 enum isl_dim_type type)
307 return n(constraint, type);
310 void isl_constraint_get_constant(struct isl_constraint *constraint, isl_int *v)
314 isl_int_set(*v, constraint->line[0][0]);
317 void isl_constraint_get_coefficient(struct isl_constraint *constraint,
318 enum isl_dim_type type, int pos, isl_int *v)
323 isl_assert(constraint->ctx, pos < n(constraint, type), return);
324 isl_int_set(*v, constraint->line[0][offset(constraint, type) + pos]);
327 struct isl_div *isl_constraint_div(struct isl_constraint *constraint, int pos)
332 isl_assert(constraint->ctx, pos < n(constraint, isl_dim_div),
334 isl_assert(constraint->ctx,
335 !isl_int_is_zero(constraint->bmap->div[pos][0]), return NULL);
336 return isl_basic_map_div(isl_basic_map_copy(constraint->bmap), pos);
339 void isl_constraint_set_constant(struct isl_constraint *constraint, isl_int v)
343 isl_int_set(constraint->line[0][0], v);
346 void isl_constraint_set_coefficient(struct isl_constraint *constraint,
347 enum isl_dim_type type, int pos, isl_int v)
352 isl_assert(constraint->ctx, pos < n(constraint, type), return);
353 isl_int_set(constraint->line[0][offset(constraint, type) + pos], v);
356 void isl_constraint_clear(struct isl_constraint *constraint)
362 total = isl_basic_map_total_dim(constraint->bmap);
363 isl_seq_clr(constraint->line[0], 1 + total);
366 struct isl_constraint *isl_constraint_negate(struct isl_constraint *constraint)
373 isl_assert(constraint->ctx, !isl_constraint_is_equality(constraint),
375 isl_assert(constraint->ctx, constraint->bmap->ref == 1, goto error);
376 total = isl_basic_map_total_dim(constraint->bmap);
377 isl_seq_neg(constraint->line[0], constraint->line[0], 1 + total);
378 isl_int_sub_ui(constraint->line[0][0], constraint->line[0][0], 1);
379 ISL_F_CLR(constraint->bmap, ISL_BASIC_MAP_NORMALIZED);
382 isl_constraint_free(constraint);
386 int isl_constraint_is_equality(struct isl_constraint *constraint)
390 return constraint->line >= constraint->bmap->eq;
393 int isl_constraint_is_div_constraint(__isl_keep isl_constraint *constraint)
399 if (isl_constraint_is_equality(constraint))
401 for (i = 0; i < constraint->bmap->n_div; ++i) {
402 if (isl_int_is_zero(constraint->bmap->div[i][0]))
404 if (isl_basic_map_is_div_constraint(constraint->bmap,
405 constraint->line[0], i))
412 /* We manually set ISL_BASIC_SET_FINAL instead of calling
413 * isl_basic_map_finalize because we want to keep the position
414 * of the divs and we therefore do not want to throw away redundant divs.
415 * This is arguably a bit fragile.
417 __isl_give isl_basic_map *isl_basic_map_from_constraint(
418 __isl_take isl_constraint *constraint)
421 struct isl_basic_map *bmap;
428 if (constraint->bmap->n_eq == 1 && constraint->bmap->n_ineq == 0) {
429 bmap = isl_basic_map_copy(constraint->bmap);
430 isl_constraint_free(constraint);
434 bmap = isl_basic_map_universe_like(constraint->bmap);
435 bmap = isl_basic_map_align_divs(bmap, constraint->bmap);
436 bmap = isl_basic_map_cow(bmap);
437 bmap = isl_basic_map_extend_constraints(bmap, 1, 1);
438 if (isl_constraint_is_equality(constraint)) {
439 k = isl_basic_map_alloc_equality(bmap);
445 k = isl_basic_map_alloc_inequality(bmap);
450 total = isl_basic_map_total_dim(bmap);
451 isl_seq_cpy(c, constraint->line[0], 1 + total);
452 isl_constraint_free(constraint);
454 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
457 isl_constraint_free(constraint);
458 isl_basic_map_free(bmap);
462 struct isl_basic_set *isl_basic_set_from_constraint(
463 struct isl_constraint *constraint)
468 isl_assert(constraint->ctx,n(constraint, isl_dim_in) == 0, goto error);
469 return (isl_basic_set *)isl_basic_map_from_constraint(constraint);
471 isl_constraint_free(constraint);
475 int isl_basic_set_has_defining_equality(
476 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
477 struct isl_constraint **c)
485 offset = basic_set_offset(bset, type);
486 total = isl_basic_set_total_dim(bset);
487 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
488 for (i = 0; i < bset->n_eq; ++i)
489 if (!isl_int_is_zero(bset->eq[i][offset + pos]) &&
490 isl_seq_first_non_zero(bset->eq[i]+offset+pos+1,
491 1+total-offset-pos-1) == -1) {
492 *c= isl_basic_set_constraint(isl_basic_set_copy(bset),
499 int isl_basic_set_has_defining_inequalities(
500 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
501 struct isl_constraint **lower,
502 struct isl_constraint **upper)
508 isl_int **lower_line, **upper_line;
512 offset = basic_set_offset(bset, type);
513 total = isl_basic_set_total_dim(bset);
514 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
516 for (i = 0; i < bset->n_ineq; ++i) {
517 if (isl_int_is_zero(bset->ineq[i][offset + pos]))
519 if (isl_int_is_one(bset->ineq[i][offset + pos]))
521 if (isl_int_is_negone(bset->ineq[i][offset + pos]))
523 if (isl_seq_first_non_zero(bset->ineq[i]+offset+pos+1,
524 1+total-offset-pos-1) != -1)
526 for (j = i + 1; j < bset->n_ineq; ++j) {
527 if (!isl_seq_is_neg(bset->ineq[i]+1, bset->ineq[j]+1,
530 isl_int_add(m, bset->ineq[i][0], bset->ineq[j][0]);
531 if (isl_int_abs_ge(m, bset->ineq[i][offset+pos]))
534 if (isl_int_is_pos(bset->ineq[i][offset+pos])) {
535 lower_line = &bset->ineq[i];
536 upper_line = &bset->ineq[j];
538 lower_line = &bset->ineq[j];
539 upper_line = &bset->ineq[i];
541 *lower = isl_basic_set_constraint(
542 isl_basic_set_copy(bset), lower_line);
543 *upper = isl_basic_set_constraint(
544 isl_basic_set_copy(bset), upper_line);
555 /* Given two constraints "a" and "b" on the variable at position "abs_pos"
556 * (in "a" and "b"), add a constraint to "bset" that ensures that the
557 * bound implied by "a" is (strictly) larger than the bound implied by "b".
559 * If both constraints imply lower bounds, then this means that "a" is
560 * active in the result.
561 * If both constraints imply upper bounds, then this means that "b" is
562 * active in the result.
564 static __isl_give isl_basic_set *add_larger_bound_constraint(
565 __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
566 unsigned abs_pos, int strict)
572 k = isl_basic_set_alloc_inequality(bset);
576 total = isl_basic_set_dim(bset, isl_dim_all);
579 isl_int_neg(t, b[1 + abs_pos]);
581 isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
582 isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
583 t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
587 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
593 isl_basic_set_free(bset);
597 /* Add constraints to "context" that ensure that "u" is the smallest
598 * (and therefore active) upper bound on "abs_pos" in "bset" and return
599 * the resulting basic set.
601 static __isl_give isl_basic_set *set_smallest_upper_bound(
602 __isl_keep isl_basic_set *context,
603 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
607 context = isl_basic_set_copy(context);
608 context = isl_basic_set_cow(context);
610 context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);
612 for (j = 0; j < bset->n_ineq; ++j) {
615 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
617 context = add_larger_bound_constraint(context,
618 bset->ineq[j], bset->ineq[u], abs_pos, j > u);
621 context = isl_basic_set_simplify(context);
622 context = isl_basic_set_finalize(context);
627 /* Add constraints to "context" that ensure that "u" is the largest
628 * (and therefore active) upper bound on "abs_pos" in "bset" and return
629 * the resulting basic set.
631 static __isl_give isl_basic_set *set_largest_lower_bound(
632 __isl_keep isl_basic_set *context,
633 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
637 context = isl_basic_set_copy(context);
638 context = isl_basic_set_cow(context);
640 context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);
642 for (j = 0; j < bset->n_ineq; ++j) {
645 if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
647 context = add_larger_bound_constraint(context,
648 bset->ineq[l], bset->ineq[j], abs_pos, j > l);
651 context = isl_basic_set_simplify(context);
652 context = isl_basic_set_finalize(context);
657 static int foreach_upper_bound(__isl_keep isl_basic_set *bset,
658 enum isl_dim_type type, unsigned abs_pos,
659 __isl_take isl_basic_set *context, int n_upper,
660 int (*fn)(__isl_take isl_constraint *lower,
661 __isl_take isl_constraint *upper,
662 __isl_take isl_basic_set *bset, void *user), void *user)
664 isl_basic_set *context_i;
665 isl_constraint *upper = NULL;
668 for (i = 0; i < bset->n_ineq; ++i) {
669 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
672 context_i = set_smallest_upper_bound(context, bset,
673 abs_pos, n_upper, i);
674 if (isl_basic_set_is_empty(context_i)) {
675 isl_basic_set_free(context_i);
678 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
680 if (!upper || !context_i)
682 if (fn(NULL, upper, context_i, user) < 0)
686 isl_basic_set_free(context);
688 if (i < bset->n_ineq)
693 isl_constraint_free(upper);
694 isl_basic_set_free(context_i);
695 isl_basic_set_free(context);
699 static int foreach_lower_bound(__isl_keep isl_basic_set *bset,
700 enum isl_dim_type type, unsigned abs_pos,
701 __isl_take isl_basic_set *context, int n_lower,
702 int (*fn)(__isl_take isl_constraint *lower,
703 __isl_take isl_constraint *upper,
704 __isl_take isl_basic_set *bset, void *user), void *user)
706 isl_basic_set *context_i;
707 isl_constraint *lower = NULL;
710 for (i = 0; i < bset->n_ineq; ++i) {
711 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
714 context_i = set_largest_lower_bound(context, bset,
715 abs_pos, n_lower, i);
716 if (isl_basic_set_is_empty(context_i)) {
717 isl_basic_set_free(context_i);
720 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
722 if (!lower || !context_i)
724 if (fn(lower, NULL, context_i, user) < 0)
728 isl_basic_set_free(context);
730 if (i < bset->n_ineq)
735 isl_constraint_free(lower);
736 isl_basic_set_free(context_i);
737 isl_basic_set_free(context);
741 static int foreach_bound_pair(__isl_keep isl_basic_set *bset,
742 enum isl_dim_type type, unsigned abs_pos,
743 __isl_take isl_basic_set *context, int n_lower, int n_upper,
744 int (*fn)(__isl_take isl_constraint *lower,
745 __isl_take isl_constraint *upper,
746 __isl_take isl_basic_set *bset, void *user), void *user)
748 isl_basic_set *context_i, *context_j;
749 isl_constraint *lower = NULL;
750 isl_constraint *upper = NULL;
753 for (i = 0; i < bset->n_ineq; ++i) {
754 if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
757 context_i = set_largest_lower_bound(context, bset,
758 abs_pos, n_lower, i);
759 if (isl_basic_set_is_empty(context_i)) {
760 isl_basic_set_free(context_i);
764 for (j = 0; j < bset->n_ineq; ++j) {
765 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
768 context_j = set_smallest_upper_bound(context_i, bset,
769 abs_pos, n_upper, j);
770 context_j = isl_basic_set_extend_constraints(context_j,
772 context_j = add_larger_bound_constraint(context_j,
773 bset->ineq[i], bset->ineq[j], abs_pos, 0);
774 context_j = isl_basic_set_simplify(context_j);
775 context_j = isl_basic_set_finalize(context_j);
776 if (isl_basic_set_is_empty(context_j)) {
777 isl_basic_set_free(context_j);
780 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
782 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
784 if (!lower || !upper || !context_j)
786 if (fn(lower, upper, context_j, user) < 0)
790 isl_basic_set_free(context_i);
792 if (j < bset->n_ineq)
796 isl_basic_set_free(context);
798 if (i < bset->n_ineq)
803 isl_constraint_free(lower);
804 isl_constraint_free(upper);
805 isl_basic_set_free(context_i);
806 isl_basic_set_free(context_j);
807 isl_basic_set_free(context);
811 /* For each pair of lower and upper bounds on the variable "pos"
812 * of type "type", call "fn" with these lower and upper bounds and the
813 * set of constraints on the remaining variables where these bounds
814 * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
816 * If the designated variable is equal to an affine combination of the
817 * other variables then fn is called with both lower and upper
818 * set to the corresponding equality.
820 * If there is no lower (or upper) bound, then NULL is passed
821 * as the corresponding bound.
823 * We first check if the variable is involved in any equality.
824 * If not, we count the number of lower and upper bounds and
827 int isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
828 enum isl_dim_type type, unsigned pos,
829 int (*fn)(__isl_take isl_constraint *lower,
830 __isl_take isl_constraint *upper,
831 __isl_take isl_basic_set *bset, void *user), void *user)
834 isl_constraint *lower = NULL;
835 isl_constraint *upper = NULL;
836 isl_basic_set *context = NULL;
838 int n_lower, n_upper;
842 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
843 isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
847 if (type == isl_dim_set)
848 abs_pos += isl_basic_set_dim(bset, isl_dim_param);
850 for (i = 0; i < bset->n_eq; ++i) {
851 if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
854 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
856 upper = isl_constraint_copy(lower);
857 context = isl_basic_set_remove(isl_basic_set_copy(bset),
859 if (!lower || !upper || !context)
861 return fn(lower, upper, context, user);
866 for (i = 0; i < bset->n_ineq; ++i) {
867 if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
869 else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
873 context = isl_basic_set_copy(bset);
874 context = isl_basic_set_cow(context);
877 for (i = context->n_ineq - 1; i >= 0; --i)
878 if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
879 isl_basic_set_drop_inequality(context, i);
881 context = isl_basic_set_drop(context, type, pos, 1);
882 if (!n_lower && !n_upper)
883 return fn(NULL, NULL, context, user);
885 return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
888 return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
890 return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
893 isl_constraint_free(lower);
894 isl_constraint_free(upper);
895 isl_basic_set_free(context);